EVALUATING THE ACCURACY OF A GRAVIMETRIC SURVEY 141 



on the character of the true field ^; / is the range of integration on the 

 profile. 



However, one of the basic problems of a gravimetric survey (if it is carried 

 out for geological purposes) is the study of the changes in the gravity anomaly 

 field from point to point. The pattern of these changes is given by the 

 gravity isoanomalies. It is important to evaluate the accuracy with which 

 these changes are determined by means of the isoanomalies. For this 

 purpose it is necessary to find the mean scjuare value of the error in deter- 

 mining the gravity increment between two neighbouring isoanomalies. Let 

 us find the inathematical expression for this error. 



iVlong the profile let there be a curve for the true value of gravity g (x) 

 and at the points x^, x^ and x.^ the obtained gravity values g-^^ g^, g^ 

 (Fig. 1). As a result of linear interpolation, we obtain an approximate ex- 

 j)ression of the function g{x) in the interval (v^, Vg) of the profile in the 

 form of a broken LMN. On the profile let us select the points A and B, 

 tt) ^vhich correspond the true values for the force of gravity gj^ and g^ and 

 tJie observed (taken with the broken LMN) values gj^ and g^. 



Let the points A and B be selected so that gB~SA ^ !'■> "^vhere p is the 

 cross-section of the isoanomalies. Then the expression 



^={gB-gA)-(SB-gA) (2) 



will give the value for the absolute error in deterniining the increase in the 

 force of gravity within the limits of two neighbouring isoanomalies. This 

 value is a function of a, a, g and p. The mean square value (we will call it 

 <5^) of this function, determined for a certain section I of the profile, can be 

 represented by the following integral expression: 



\j^no.a. 



9(v),/>]d.v. (3) 



As will be showii, the tw^o criteria proposed for evaluating the accuracy 

 of a gravimetric map— from the mean square error in the value of gravity 

 at an arbitrary point of the map (f^) and from the value of the mean 

 square error in determining the gravity increment between limits of two 

 neighbouring isoanomalies (5^^) are in practice sufficient for solving all basic 

 problems connected with an evaluation of the quality of work carried out 

 and for the determination of the necessary parameters of the survey at the 

 planning stage. 



The indices of accuracy e^^^ and d^ give the absolute value of the errors. 

 However, in practice, anomaly fields with differing intensities are encoun- 



